There are a couple of issues here:
1) Romo doesn't make Cleveland very competitive. They have way too many holes that are going to take a couple of offseasons to fix before they could be considered competitive. So that's one big reason they would have no interest in Romo.
2) Romo's cap number would be $14MM next year based on his current deal. If the Browns take Watson or Kizer with their first pick next year, his cap number will be around $5-6MM. So for at least the few years Romo would play, no his cap number is not as favorable as if they took their next franchise QB in the draft.
3) Three, they've brought in baseball people to bring analytics into football. They've been about accumulating as many high picks as they can get. They aren't about to turn around and trade a high first round pick for an aging QB coming off two injury plagued years.
The Browns simply aren't in the position where taking Romo on would make sense.
In the end, this really isn't my overarching point. I think there is definitely a chance Romo could be traded. I do believe someone out there might take a chance on him. Where my issue comes in is the belief that he's uber valuable to the point where he's worth multiple first round picks and how there will be so many teams after him. I don't believe there is any chance in hell that's the case given his age and injury history.
So he might get moved but the compensation isn't going to be as high as you think. I'll put it another way. I like Romo but if someone came to the Cowboys and offered say a 2nd round pick for him and then maybe a conditional pick that could turn into another 2nd rounder.......... I'd think long and hard about taking that deal.